Under very general assumptions on the underlying theory (see [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]} and references therein), we can determine the composition and spectra of the standard model particles produced by the SHDM decay. Typical decay products are couples of quark and anti-quark that, through a cascading process (jets), give rise to neutrinos, gamma rays and nucleons with a flat spectrum, that at the relevant energies can be approximated as \(dN/dE \propto E^{-1.9}\) , independently of the particle type, with a photon/nucleon ratio of about \(\gamma /N\simeq 2\div 3\)  and a neutrino nucleon ratio \(\nu /N\simeq 3\div 4\) , quite independent of the energy range [4]}. The most constraining limits on the SHDM mass and lifetime are those coming from the (non) observation of UHE photons and, even to a lesser extent, neutrinos in the UHECR regime. Auger observations provide us with very stringent limits on the photon and neutrino fluxes in the energy range \(10^{8}\div 10^{11}\)  GeV, enabling far the best limits on SHDM models [2]}, [3]}.
